Conventionally, an electric power steering apparatus includes an electric motor for assisting a driver's steering wheel operation, and an electronic control unit (hereinafter referred to as the “ECU”) for driving and controlling the electric motor while setting a target assist torque corresponding to a steering torque applied to the steering wheel by the driver. An electric power steering apparatus which employs a brushless DC motor as the electric motor is also widely used. In such a brushless DC motor, electricity is supplied to U-phase, V-phase, and W-phase coils through switching control of an inverter. The brushless DC motor is driven through current vector control which uses a d-q coordinate system. The d-axis of the coordinate system corresponds to the penetrating direction of a magnetic field of a permanent magnet provided on a rotor of the motor, and the q-axis of the coordinate system is orthogonal to the d-axis. Accordingly, in the case where such a brushless DC motor is used, a rotational angle sensor is provided so as to detect the electrical angle of the rotor.
When the rotational angle sensor fails, control of the motor becomes impossible. An electric power steering apparatus which can solve this problem has been known (for example, see Japanese Patent Application Laid-Open (kokai) No. 2008-37399). When the rotational angle sensor fails, the known electric power steering apparatus estimates the electrical angle from an inductive voltage (counter electromotive force) generated in the motor, and drives and controls the motor through use of the estimated electrical angle (estimative electrical angle). Motor control which utilizes such an estimative electrical angle is called sensorless control. When the sensorless control is performed, an ECU estimates the d-axis and the q-axis on the basis of the estimative electrical angle, and performs current vector control through use of the estimated d-q coordinate system. The estimated d-axis for control will be referred to as the “γ-axis,” and the estimated q-axis for control will be referred to as the “δ-axis.”